95 lines
2.3 KiB
Python
95 lines
2.3 KiB
Python
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from heapq import heappush, heappop
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from collections import deque
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from fixtures import weighted_graph, expanded_weights_graph
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# UnweightedGraph(a) :: Map(a, Set(a))
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# WeightedGraph(a) :: Map(a, Set(a))
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# shortest_path_dijkstra :: Vertex -> Vertex -> WeightedGraph(Vertex)
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def shortest_path_dijkstra(a, b, g):
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q = []
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seen = set()
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heappush(q, (0, a, [a]))
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while q:
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w0, v0, path = heappop(q)
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if v0 in seen:
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continue
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elif v0 == b:
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return w0, path
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for w1, v1 in g.get(v0):
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heappush(q, (w0 + w1, v1, path + [v1]))
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seen.add(v0)
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return 'weighted', 'pizza'
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# expand_edge :: Vertex -> (Weight, Vertex) -> Map(Vertex, [Vertex])
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def expand_edge(v0, wv):
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w, v1 = wv
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assert w > 1
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result = {v0: ['{}-{}'.format(v1, 1)]}
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for x in range(w - 2):
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result['{}-{}'.format(v1, x + 1)] = ['{}-{}'.format(v1, x + 2)]
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result['{}-{}'.format(v1, w - 1)] = [v1]
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return result
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# expand_weights :: Vertex -> WeightedGraph(Vertex) -> UnweightedGraph(Vertex)
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def expand_weights(v, g):
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result = {}
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q = deque()
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seen = set()
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q.append(v)
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while q:
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v = d.popleft()
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if v in seen:
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continue
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x = expand_edge(v, g.get)
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for w, v1 in g.get(v):
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if w > 1:
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ws = expand_edge(v, (w, v1))
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result = {**result, **ws}
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q.append(v)
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pass
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# shortest_path_inject :: Vertex -> Vertex -> WeightedGraph(Vertex)
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def shortest_path_inject(a, b, g):
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q = deque()
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seen = set()
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q.append((a, [a]))
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while q:
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v0, path = q.popleft()
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if v0 == 'dummy':
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continue
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elif v0 in seen:
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continue
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elif v0 == b:
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return len(path), path
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for _, v1 in g.get(v0):
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q.append((v1, path + [v1]))
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seen.add(v0)
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continue
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return None, None
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print(expand_edge('a', (4, 'b')))
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print(expand_edge('a', (5, 'e')))
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assert expand_weights('a', weighted_graph) == expanded_weights_graph
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# a = 'a'
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# b = 'd'
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# w, x = shortest_path_dijkstra(a, b, weighted_graph)
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# w1, x1 = shortest_path_inject(a, b, weighted_graph)
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# print("[dijkstra] Shortest path from {} to {} is {} with weight {}".format(
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# a, b, x, w))
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# print("[injection] Shortest path from {} to {} is {} with weight {}".format(
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# a, b, x1, w1))
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